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Selection Theorem for Systems with Inheritance

A. N. Gorban (2010)

Mathematical Modelling of Natural Phenomena

The problem of finite-dimensional asymptotics of infinite-dimensional dynamic systems is studied. A non-linear kinetic system with conservation of supports for distributions has generically finite-dimensional asymptotics. Such systems are apparent in many areas of biology, physics (the theory of parametric wave interaction), chemistry and economics. This conservation of support has a biological interpretation: inheritance. The finite-dimensional asymptotics demonstrates effects of “natural”...

Selections and suborderability

Giuliano Artico, Umberto Marconi, Jan Pelant, Luca Rotter, Mikhail Tkachenko (2002)

Fundamenta Mathematicae

We extend van Mill-Wattel's results and show that each countably compact completely regular space with a continuous selection on couples is suborderable. The result extends also to pseudocompact spaces if they are either scattered, first countable, or connected. An infinite pseudocompact topological group with such a continuous selection is homeomorphic to the Cantor set. A zero-selection is a selection on the hyperspace of closed sets which chooses always an isolated point of a set. Extending Fujii-Nogura...

Selivanovski hard sets are hard

Janusz Pawlikowski (2015)

Fundamenta Mathematicae

Let H Z 2 ω . For n ≥ 2, we prove that if Selivanovski measurable functions from 2 ω to Z give as preimages of H all Σₙ¹ subsets of 2 ω , then so do continuous injections.

Semi-contractions des espaces localement compacts et cas des variétés complexes

Jean-Jacques Loeb (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

En nous inspirant d’articles de Beardon, nous donnons des résultats concernant les points fixes et les orbites d’auto-applications contractantes et semi-contractantes des espaces connexes localement compacts. Des résultats plus précis sont obtenus dans le cas des variétés complexes Kobayashi hyperboliques.

Semigroup actions on tori and stationary measures on projective spaces

Yves Guivarc'h, Roman Urban (2005)

Studia Mathematica

Let Γ be a subsemigroup of G = GL(d,ℝ), d > 1. We assume that the action of Γ on d is strongly irreducible and that Γ contains a proximal and quasi-expanding element. We describe contraction properties of the dynamics of Γ on d at infinity. This amounts to the consideration of the action of Γ on some compact homogeneous spaces of G, which are extensions of the projective space d - 1 . In the case where Γ is a subsemigroup of GL(d,ℝ) ∩ M(d,ℤ) and Γ has the above properties, we deduce that the Γ-orbits...

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